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, , Mechanics: is a branch of physics that deals, with the conditions of rest or motion of the, material objects around us., , Motion: An object is said to be in motion if it, changes its position with respect to its, surroundings with the passage of time.,  Rest: An object is said to be at rest if it does not, change its position with respect to its, surroundings with passage of time., 

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Motion is a relative term, Motion of an object is always with respect, to some Frame of reference.,  Frame of reference, 

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MOTION IN 1-D, 2-D AND 3-D, , , One dimensional motion: (Motion in a straight line), The motion of an object is said to be one, dimensional if only one of the three Co-ordinates, specifying the position of the object changes with, time.

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, , Two dimensional motion: (Motion in a Plane), The motion of an object is said to be two, dimensional if only two of the three Co-ordinates, specifying the position of the object changes with, time.

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, , Three dimensional motion: (Motion in Space), The motion of an object is said to be three, dimensional if all the three Co-ordinates specifying, the position of the object, changes with time.

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Scalars: A scalar quantity is defined as the, physical quantity that has only magnitude (or, numerical value)., ➢ Examples: Mass, Time , Volume , Speed,, Temperature , Distance, Entropy, Energy , Work,, etc.,  Vectors: A vector quantity is defined as the, physical quantity that has both magnitude as, well as direction., ➢ Examples: Force, Velocity, Acceleration,, Displacement, Momentum, etc., 

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Difference between Scalars and Vectors, Scalars, 1. They have only, magnitude., 2. They change if their, magnitude changes., , Vectors, 1. They have both magnitude, and direction, 2. They change if either their, magnitude, direction or both, changes., 3. They can be added, 3. They can be added only by, according to ordinary laws of using special laws of vector, algebra., addition., Note: Physical quantities which have no specified direction, and have different values in different directions are called, Tensors. For example: Moment of Inertia

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Representation of a Vector, , Length of vector gives its Magnitude and arrow, head gives its Direction.

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Position and Displacement Vectors, , , Position Vector: It is a vector which gives position of an, object with reference to the origin of a co-ordinate system., It is represented by a straight line between the origin and, the position at time ‘t’., , , , Displacement Vector: It is that, vector which tells how much, and in which direction an object, has changed its position in a, given time interval.

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Some terms in Vector Algebra, 1., , Equal Vectors:, , , , Equal vectors are vectors that have the same, magnitude and the same direction., Equal vectors may start at different positions., Note that when the vectors are equal, the directed line, segments are parallel., , , , 

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2., , Negative of a Vector:, Negative of a Vector is defined as another vector having, same magnitude but opposite direction., , 3., , Modulus of a Vector:, It is the length ( Numerical value), or the magnitude of that vector., It is a Scalar quantity., , Modulus of Vector A = A = A

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4. Unit Vector,  A unit vector is a vector of unit (one) magnitude drawn, in the direction of a given vector.,  A unit vector is denoted by a cap over head (â)., , , ˆ = A, A, , A

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5. Collinear Vectors:, The vectors which either act along the same line or, along parallel lines are called Collinear Vectors., , Like or Parallel Collinear Vectors, , Unlike or Antiparallel Collinear Vectors, , Two Vectors having same direction, , Two vectors having the opposite direction, ,  = 0, ,  = 180, A, A, , example:, , , A, , A, B, , , B, , , B, , , B

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6. Fixed vector: The vectors whose initial point, is fixed., 7. Free vector: The vector whose initial point is, not fixed., 8. Co-planar vectors: The vectors which act in, the same plane., 9. Co-initial vectors: The vectors which have, the same initial points., 10. Co-terminus vectors: The vectors which have, the common terminal point.

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Zero Vector or Null Vector,  A zero or Null vector is a vector that has zero, magnitude and an arbitrary direction., ,  It is represented by 0., ➢ Properties of Zero Vector:, i. When a vector is added to zero vector, we get, the same vector.,   , A+0 = A, ii. When a real number is multiplied by a zero, vector, we get a zero vector.,  , 0 = 0, iii. When a vector is multiplied by zero, we get a, zero vector.  , 11., , 0A = 0

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➢ Physical, 1., 2., , 3., , ➢, , examples of Zero Vector:, , The position vector of a particle lying at the origin, is a Zero vector., The velocity vector of a stationary object is a Zero, vector., The acceleration vector of an object moving with, uniform velocity is a Zero vector., , Physical meaning of Zero Vector:, If an object which is at point P at time t1 goes to, point Q at time t2 and then comes back to point P at, time t3, then its Displacement is????, Zero, i.e. a Zero vector or Null vector, as Displacement is a vector quantity.